The Big Idea
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Problem 3.1
Notes: Each large table holds 10 people and is served 4 pizzas. Each small table holds 8 people and is served 3 pizzas.
A.If the pizzas are shared equally by everyone at the table, will a person sitting at a small table get the same amount of pizza as a person sitting at the large table? Explain your reasoning.
A person sitting at a small table will not have as much pizza as someone in the large table. There are 10 people and 4 pizzas at the large table and 8 people and 3 pizzas in the small table. If I divide 4 by 10 I get .4 and that means each person at the large table gets .4 of a pizza. If I divide 3 by 8 I get .375 of a pizza and .375 is less than .4 so a person at large table gets more.
B.The ratio of large tables to small table is 8 to 5. There are exactly enough seats for 240 campers. How many tables of each kind are there?
The ratio of large tables to small tables is 8:5. If there are enough seats for 240 campers there will be 16 large tables and 10 small tables. 8 large tables hold 80 people (8x10) and 5 small tables hold 40 people (5x8). 80+40= 120 seats. 240/120=2. 80x2=160 and 160 seats means 16 large tables (160/10). 40x2=80 and 80 seats means 10 small tables (80/8).
3.1 Follow-Up 1.How were ratios helpful in thinking about the problem?
Ratios were helpful in thinking about the problem because I could add the two numbers of a part-to-part ratio to find the total. Then from there, I could use fractions now that I know the total and I could compare the fractions to other ratios by finding the lowest common denominator. I could even use decimals by dividing the part by the total.
2.How many pizzas will the cook need to make in order to put 4 pizzas on each large table and 3 pizzas in each small table?
The cook would need to make 64 pizzas for the large tables and 30 pizzas for the small tables. I just multiplied the number of table (16 large and 10 small) by the number of pizzas at each table (4 for large table and 3 for small table). So to find how many pizzas are needed for the large tables, I did 16x4 and got 64. And to find how many pizzas are needed for the small tables, I did 10x3 and got 30.
Ajwad Khan
Nov. 23, 09
Math 7B
The Big Idea
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Problem 3.1
Notes: Each large table holds 10 people and is served 4 pizzas. Each small table holds 8 people and is served 3 pizzas.
A. If the pizzas are shared equally by everyone at the table, will a person sitting at a small table get the same amount of pizza as a person sitting at the large table? Explain your reasoning.
A person sitting at a small table will not have as much pizza as someone in the large table. There are 10 people and 4 pizzas at the large table and 8 people and 3 pizzas in the small table. If I divide 4 by 10 I get .4 and that means each person at the large table gets .4 of a pizza. If I divide 3 by 8 I get .375 of a pizza and .375 is less than .4 so a person at large table gets more.
B. The ratio of large tables to small table is 8 to 5. There are exactly enough seats for 240 campers. How many tables of each kind are there?
The ratio of large tables to small tables is 8:5. If there are enough seats for 240 campers there will be 16 large tables and 10 small tables. 8 large tables hold 80 people (8x10) and 5 small tables hold 40 people (5x8). 80+40= 120 seats. 240/120=2. 80x2=160 and 160 seats means 16 large tables (160/10). 40x2=80 and 80 seats means 10 small tables (80/8).
3.1 Follow-Up
1. How were ratios helpful in thinking about the problem?
Ratios were helpful in thinking about the problem because I could add the two numbers of a part-to-part ratio to find the total. Then from there, I could use fractions now that I know the total and I could compare the fractions to other ratios by finding the lowest common denominator. I could even use decimals by dividing the part by the total.
2. How many pizzas will the cook need to make in order to put 4 pizzas on each large table and 3 pizzas in each small table?
The cook would need to make 64 pizzas for the large tables and 30 pizzas for the small tables. I just multiplied the number of table (16 large and 10 small) by the number of pizzas at each table (4 for large table and 3 for small table). So to find how many pizzas are needed for the large tables, I did 16x4 and got 64. And to find how many pizzas are needed for the small tables, I did 10x3 and got 30.